On the cause of Zeta potential of a charged vesicle. The extra- and intravesicular membrane charges contribute differently to the extra- and intravesicular potential

TL;DR

This study investigates how the contributions of intra- and extravesicular membrane charges to vesicle potential vary with electrolyte concentration, membrane curvature, and distance from the vesicle center, revealing complex potential behaviors.

Contribution

It provides a detailed analysis of how membrane charge contributions to vesicle potential depend on electrolyte concentration and spatial factors, highlighting differences from simplified assumptions.

Findings

At low electrolyte concentrations, Vex/Vin>1 and increases with distance.

At high electrolyte concentrations, Vex/Vin varies non-monotonically with distance.

Charge contributions from inner and outer surfaces differ significantly depending on conditions.

Abstract

When the charge densities on the inner and outer surface of the vesicle membrane are similar one may assume that the potential at a point closer to the outer/inner surface is more affected by the charges located at the outer/inner surface of the vesicle membrane. However, because of the curvature of the vesicle and the screening effect of the electrolyte ions the situation is more complicated. When the charge densities at the inner and outer surface of the vesicle membrane are the same then at any finite distance Z from the center of the vesicle the contribution of the charges, located at the outer membrane surface, to the vesicle potential Vex is different from the contribution of the charges, located at the inner membrane surface, to the vesicle potential Vin. At low electrolyte ion concentrations (from C=0 to 0.00001 [Mol]) Vex/Vin>1 and increases with increasing distance from the center of the vesicle until the external surface of the vesicle membrane. With further increasing distance Vex/Vin remains constant at C=0 [Mol], while at C>0 [Mol] it starts decreasing. However, at high electrolyte ion concentrations (C>0.01 [Mol]) with increasing distance from the center of the vesicle Vex/Vin reaches its maximum at the internal surface of the vesicle membrane. With further increasing distance, close to the outer surface of the vesicle Vex/Vin becomes less than 1 (i.e. the charges at the inner surface of the membrane contribute to the potential more than the charges at the outer surface). Further increasing the distance Vex/Vin reaches its minimum and then increases to 1 (i.e. the charges at the inner surface of the membrane contribute to the potential like the charges at the outer surface of the membrane). With increasing electrolyte ion concentration the minimum of Vex/Vin is getting deeper (approaching zero) and its location is getting closer to the outer surface of the vesicle.